In my GelColor instruction booklet from OPI it gives cure times for the OPI LED (30 secs each layer) and the OPI Axxium UV light (1-2-3 mins for base, colour and top). It then says "Cure times may vary with non-OPI UV lights." [italics theirs]

My interpretation of that is that while the OPI lights are recommended, that other lights can be used. Still, the OPI LED and Gelcolor were made for each other and will probably give the best result.